To prepare the mashed potatoes, heat the oven to 400 degrees. Wash 2 large heads of garlic. Cut across the top of the head just enough to expose the cloves. Place a 6-inch square of heavy-duty aluminum foil on your work surface and place the heads of garlic on the foil, cut side up. Drizzle with a little olive oil and enclose the garlic completely by bringing the foil up and over, crimping the top. Place in the oven and roast until tender, about a half an hour. When done, set aside until the garlic is cool enough to handle, then squeeze the softened garlic cloves into a small bowl. Mash until smooth and set aside. Next, purée enough roasted green chile to make 2 tablespoons.

Meanwhile, boil the potatoes in salted water until they are tender, about 15 minutes. Drain the potatoes and transfer them to a baking sheet. Place in the oven for about 10 minutes to dry the potatoes. Transfer them to a large bowl and add the milk and butter. Using an electric mixer or a potato masher, combine ingredients until smooth. Add 2 tablespoons each of the roasted garlic and the green chile purée and mix until incorporated. Season to taste. Sprinkle with cheese.

Heat 3 cups milk over hot water in top of double boiler. Mix cornmeal with remaining milk and salt; add to hot milk in double boiler. Cook, stirring, until thickened. Cover and cook for another 5 minutes. Add corn and cook for 3 minutes longer. Add butter and stir until butter has melted. Fold in beaten eggs. Transfer mixture to a greased 2-quart casserole. Bake at 375 degrees F for 1 hour, or until firm but light (It will sink when removed from oven). Serve immediately with butter.